Advertisements
Advertisements
Question
If the volume of a cuboid is 3x2 − 27, then its possible dimensions are
Options
3, x2, − 27x
3, x − 3, x + 3
3, x2, 27x
3, 3, 3
Advertisements
Solution
We have to find the possible dimension of cuboid
Given: volume of cuboid `3x^2 - 27`
`3x^2 -27 = 3x^2 - 3xx 3 xx 3`
` = 3x^2 - 3 xx 3 xx 3`
Take 3 as common factor
`3x^2 - 27 = 3(x^2 - 3^2)`
Using identity `x^2 -y^2 = (x+y)(x-y)`
We get,
`3x^2 - 27 =3(3x+3) (x-3)`
Here the dimension of cuboid is 3,3, x + 3, x - 3
APPEARS IN
RELATED QUESTIONS
Expand the following, using suitable identity:
(–2x + 5y – 3z)2
Evaluate the following using suitable identity:
(99)3
If x + y + z = 0, show that x3 + y3 + z3 = 3xyz.
Simplify the following
`(7.83 + 7.83 - 1.17 xx 1.17)/6.66`
If 3x - 7y = 10 and xy = -1, find the value of `9x^2 + 49y^2`
Simplify the following products:
`(x/2 - 2/5)(2/5 - x/2) - x^2 + 2x`
If \[x^2 + \frac{1}{x^2}\], find the value of \[x^3 - \frac{1}{x^3}\]
Evaluate of the following:
(99)3
Find the value of 27x3 + 8y3, if 3x + 2y = 14 and xy = 8
Find the value of 27x3 + 8y3, if 3x + 2y = 20 and xy = \[\frac{14}{9}\]
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{x}{7} + \frac{y}{3} \right) \left( \frac{x^2}{49} + \frac{y^2}{9} - \frac{xy}{21} \right)\]
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{x}{y} - \frac{y}{3} \right) \frac{x^2}{16} + \frac{xy}{12} + \frac{y^2}{9}\]
Find the square of : 3a - 4b
Evaluate: (4 − ab) (8 + ab)
Expand the following:
(2x - 5) (2x + 5) (2x- 3)
Evaluate the following without multiplying:
(1005)2
If a - b = 10 and ab = 11; find a + b.
If x + y = 1 and xy = -12; find:
x2 - y2.
If a2 - 3a - 1 = 0 and a ≠ 0, find : `"a"^2 - (1)/"a"^2`
Factorise the following:
4x2 + 20x + 25
